Haviside and Related Functions

Description

A collection and description of functions which compute the Heaviside and related functions, the sign function, the delta function, the boxcar function, and the ramp function.

The functions are:

Usage

H(x, a = 0)
Sign(x, a = 0)
Delta(x, a = 0)
Boxcar(x, a = 0.5)
Ramp(x, a = 0)

Arguments

Details

The Heaviside step function H is 1 for x>a, 1/2 for x=a, and 0 for x<a.

The Sign function Sign is 1 for x>a, 0 for x=a, and -1 for x<a.

The delta function Delta is defined as: Delta(x) = d/dx H(x-a).

The boxcar function boxcar is defined as: Boxcar(x) = H(x+a) - H(x-a).

The ramp function is defined as: Ramp(x)= (x-a)*H(x-a).

Value

returns the function values of the selected function.

Author(s)

Diethelm Wuertz for the Rmetrics R-port.

References

Weisstein W. (2004); http://mathworld.wolfram.com/HeavisideStepFunction.html. Mathworld.

Examples

## H -
   x = sort(round(c(-1, -0.5, 0, 0.5, 1, 5*rnorm(5)), 2))
   h = H(x)
        
## Sign -
   s = Sign(x)
   
## Delta -
   d = Delta(x)
   
## Boxcar -
   Pi = Boxcar(x)

## ramp - 
   r = Ramp(x)
   cbind(x = x, Step = h, Signum = s, Delta = d, Pi = Pi, R = r)